A note on explicit bounds for a stopped Feynman–Kac functional

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• 作者：Cloud Makasu
• 关键词：Geometric Brownian motions ; Optimal stopping inequality
• 刊名：Statistics and Probability Letters
• 出版年：2010
• 出版时间：1 December 2010-15 December 2010
• 年：2010
• 卷：80
• 期：23-24
• 页码：1977-1979
• 全文大小：185 K

文摘

Let Q_t=(x_t,y_t) be a two-dimensional geometric Brownian motion which is possibly correlated starting at (x,y) in the positive quadrant, and let τ be an -stopping time generated by the process Q_t. Under certain conditions, we prove that where Φ is a bounded Borel function, C>0, μ>1, n>1 are constants and g_* is an explicit bound for a solution of a certain second order ordinary differential equation.

The present result extends and supplements the explicit upper bound in Hu and Øksendal (1998).